ayor Michael R. Bloomberg has a golf date planned with Assembly Speaker Sheldon Silver on Thursday. More than eagles and birdies, the between-holes talk among the two will almost certainly be about whether Mr. Silver will sign off on the mayor's plan for a West Side stadium.

It is no coincidence that the stadium's future happens to depend in large part upon Mr. Silver, who effectively controls a third of the state's Public Authorities Control Board, which has final say over the stadium plan and could vote on its future as early as May 18.

The golf game will be just the latest in a long but intensifying courtship of Mr. Silver by city and state officials. There was a meeting last week with the deputy mayor for economic development and rebuilding, Daniel L. Doctoroff, and a dinner the week before that with Mr. Bloomberg at one of Mr. Silver's favorite kosher restaurants downtown, Noah's Ark.

In the past year or so, Mr. Bloomberg has also attended a bris for one of Mr. Silver's grandsons and visited Mr. Silver and his family when his brother died last year.

City and state officials privately acknowledge that family, food and golf are not the real keys to Mr. Silver's support - and that goodies for his district and attention to his priorities are. To that end, they are fast trying to figure out how to please Mr. Silver enough to persuade him to sign off on the stadium plan.

Their task is becoming ever more urgent: Officials say they are eager to win approval for the stadium before July, when the International Olympic Committee will decide whether to hold the 2012 Summer Games here. Mr. Bloomberg says the decision could hinge upon whether the city can guarantee that it will have a new arena.

City officials predict that the stadium will win approval soon because lawmakers will agree with the mayor that it is urgently needed to spur West Side redevelopment. "The mayor is confident that this project is in the best interests of the city and will be approved on its merits," said Edward Skyler, Mr. Bloomberg's press secretary.

He said the mayor's frequent visits with Mr. Silver were part of a blooming friendship - underscored by Mr. Silver's occasional compliments of his leadership style. And a spokesman for Mr. Silver said they shared "a certain degree of mutual respect and affinity."

Playing the sought-after belle of the ball, Mr. Silver has been musing recently that he sees no need to rush consideration of the stadium plan. And with the stakes rising each day, he seems to be getting his way on matters he has long groused about.

Just a couple of months ago, Mr. Silver complained in an interview about a number of needs in his district - which includes much of Lower Manhattan - that he considered unmet by the city and the state. He expressed displeasure that plans for a badly needed elementary school were "stalled."

And he said that City Hall had not responded to his urgent requests that it reopen the section of Park Row that was closed after 9/11, something Chinatown business owners complained had hurt their businesses.

A few weeks later, Mr. Bloomberg appeared with Mr. Silver downtown to announce that the city would spend $65 million to build the school, which will be part of a residential and commercial tower rising on Beekman Street. Earlier this month, the mayor appeared with Mr. Silver at City Hall to announce the reopening of Park Row.

In both cases, Mr. Silver and Mr. Bloomberg chided reporters for asking whether the sudden movement on the projects had anything to do with the stadium. And state officials said plans to give tax breaks to businesses in Chinatown under a newly created economic development zone were made on the merits, pleasing as they might be to Mr. Silver.

Still, in an interview on NY1 News on Thursday, Mr. Silver indicated that he saw no need for a quick vote on the project by the Public Authorities Control Board, which is controlled by him, the Senate majority leader, Joseph L. Bruno, and Gov. George E. Pataki.

"I don't see the necessity," he said. "Senator Bruno has indicated he doesn't see the necessity, and we may not have it before July."

While Mr. Bruno has indeed indicated that he sees no rush, officials close to the deliberations say they believe he will come around under pressure from Mr. Pataki and Mr. Bloomberg, both fellow Republicans. (One complicating factor: the lobbying firm of Mr. Bruno's son, Kenneth Bruno, has Cablevision, a prominent opponent of the stadium plan, as a client.)

Although officials wonder just what Mr. Silver, a Democrat, wants in exchange for his support, he insists that he has no price, arguing that the stadium must stand on its own, while expressing reservations about its impact on the economy and on traffic. He has also complained that the mayor's West Side development proposal, which includes new office towers, would compete with the rebuilding of downtown.

So perhaps it should come as no surprise that administration officials seem to be turning their attention downtown. For instance, Mr. Silver said in an interview that at their meeting last week, he and Mr. Doctoroff discussed various proposals for tax and cash incentives to attract commercial tenants to Lower Manhattan.

"The word stadium never came up," Mr. Silver said. But a downtown rebuilding plan "should've been in place already," he said. "It has nothing to do with a stadium."

It remains unclear whether the mayor will win Mr. Silver's support for the stadium. One former city official and longtime associate of the speaker's said that despite the conventional wisdom that Mr. Silver is holding out for his own district, he is also bound by party loyalties - all of his members representing the West Side are against the stadium.

"Forgetting anything else for the speaker," the associate said, "to overrule them would be a real breach."